The logarithmic super divergence and asymptotic inference properties

Abstract

Statistical inference based on divergence measures have a long history. Recently, Maji et al. (The logarithmic super divergence and its use in statistical inference, Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, India, 2014a) have introduced a general family of divergences called the logarithmic super divergence family. This family acts as a superfamily for both the logarithmic power divergence family (eg., Renyi, Proceedings of 4th Berkeley symposium on mathematical statistics and probability, vol. I, pp. 547–561, 1961) and the logarithmic density power divergence family introduced by Jones et al. (Biometrika 88:865–873, 2001). In this paper, we describe the asymptotic properties of the inference procedures based on these divergences in discrete models. The performance of the method is demonstrated through real data examples.